Inclined Plane Push and Hold Force

Skidding a crate up a loading ramp, sizing a winch or come-along pull, or checking whether a parked load will slide. To push UP at steady speed F = W(sin theta + mu cos theta), the load's own down-slope pull plus friction on the normal W cos theta; the ideal frictionless advantage is 1/sin theta = ramp length/rise, so a longer, shallower ramp trades distance for force. Whether the load self-holds is set by the angle of repose atan(mu): below it the load is self-locking (it takes a push to send it DOWN); above it the load slides and must be restrained. A 1,000 lb crate on a 20-degree ramp at mu 0.3 takes 624 lb to push up (advantage 1.6), sits above its 16.7-degree repose angle so it slides, and needs 60 lb to hold. Rigid load, dry friction, force parallel to the incline; rolling resistance, tackle reeving, and tipping are separate. A planning aid; the rigging plan and a competent person govern.

F_up = W(sin theta + mu cos theta); normal = W cos theta; net down-slope = W(sin theta - mu cos theta); ideal MA = 1/sin theta = length/rise; self-slide at atan(mu).

Inclined-plane statics - force up the incline W(sin theta + mu cos theta) and the angle of repose atan(mu) (standard mechanics; Machinery's Handbook), by name.

Inclined-plane statics is a standard published result; the weight, angle, and friction coefficient are the user's inputs.

Estimate. AHJ and licensed professional govern.

Field names used by the API: weight_lb, incline_angle_deg, friction_coefficient, force_up_lb, normal_force_lb, ideal_mechanical_advantage

• Push-up force F = W(sin theta + mu cos theta), force parallel to the inclineMachinery's Handbook
• Self-locking self-locking below the angle of repose atan(mu); slides above itfriction mechanics
• Scope rigid load, dry friction; rolling resistance, tackle reeving, tipping, starting friction are separatescope of this tile